How to use the linear equation solver
Enter a one-variable linear equation in the form ax + b = cx + d as four numbers and the tool solves it. For something like 2x + 3 = 8, where the right side has no x, enter 0 for c and 8 for d. The calculator first rearranges both sides into (a − c)x = d − b and then splits into three cases based on the coefficient difference and the constant difference.
First, if a − c is not zero there is exactly one solution, x = (d − b)/(a − c). Second, if a − c is zero and d − b is zero as well, the two sides are the same expression and every real number is a solution. Third, if a − c is zero but d − b is not, the variable cancels and a false statement remains, so there is no solution. Zero is tested by absolute value against 1e-9 rather than with an equality check, so decimal inputs are classified correctly.
The solution is shown to 8 significant digits, and when all four inputs are whole numbers a reduced fraction appears on an extra row: 6x + 0 = 4x + 3 reports both 1.5 and 3/2. The final check row substitutes the solution back into the original left and right sides so you can see that the two values agree. Systems with two or more unknowns and equations of degree two or higher are not supported.
Frequently Asked Questions
Yes. Enter the four values in the form ax + b = cx + d and it rearranges to (a − c)x = d − b. If the right side has no x, enter 0 for c.
Both happen when the coefficient difference a − c is 0. If the constant difference d − b is also 0 the equation is an identity and every real number works; otherwise it is a contradiction with no solution.
Yes. When all four inputs are whole numbers the reduced fraction is shown as well, so 6x = 4x + 3 reports 3/2.